Locations of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem Under Radiation and Oblateness Effects

Abstract

This study deals with the generalization of the Elliptic Restricted Three-Body Problem (ER3BP) by considering the effects of radiation and oblate spheroid primaries. This may illustrate a gas giant exoplanet orbiting its host star with eccentric orbit. In the three dimensional case, this generalization may possess two additional equilibrium points (L 6,7 , out-of-plane). We determine the existence of L 6,7 in ER3BP under the effects of radiation (bigger primary) and oblateness (small primary). We analytically derive the locations of L 6,7 and assume initial approximations of (µ − 1, ± √ 3A 2 ), where µ and A 2 are the mass parameter and oblateness factor, respectively. The fixed locations are then determined. Our results show that the locations of L 6,7 are periodic and affected by A 2 and the radiation factor (q 1 ).

Stability Analysis of Modified Circular Restricted Three Body Problem by Lyapunov Exponent Indicators

“…For instance, the radiation pressure has to be incorporated when the primaries emit radiation such as the stars [4,5,6]. The non-spherical nature of stars and planets, referred to as oblateness, has been taken into account [7,8,9]. Additionally, the perturbing effects of a disk-like structure near a three-body system have been incorporated by various authors [10,2,11,12].…”